Preliminary report, Effect of climatic extremes on community stability and its drivers

1 Introduction

The following text originally came from the Ghosh UZH UFO application

As the global climate is experiencing more heat, and less rainfall - it is reasonable to expect that the distributions of these variables (temperature and rainfall) are becoming more skewed and asymmetric towards the extreme values (see figure 1.1 below, which comes from the UZH UFO proposal, where it was figure 2). With the availability of more open access long-term databases, it is possible to address how different taxa respond at the community level.

Figure 1.1: Introduction figure

As a preliminary work, I have already gathered long-term (median of 41 years) species-level abundance data for 2043 terrestrial and 716 aquatic communities. My recent result (manuscript in preparation) shows that the community stability is different for terrestrial and freshwater taxa and could be better explained considering the different strengths between pairwise species associations at the extremes, called community-level tail association, than with classic correlates of community stability studies (richness and variance ratio).

I will gather global data for annual temperature and rainfall from open access CHELSA database19 and ask how variability in temperature and precipitation would affect terrestrial taxa (birds, mammals, invertebrates, plants). For freshwater taxa (fish, phytoplankton, invertebrates), mostly temperature variability would be considered. In marine realm, sampling is spatially not consistent over the years20 and also very few long-term (>20yrs) data sampled compared to terrestrial and freshwater, thus I will focus only on the latter two realms. Also, species-level biomass (or body size) data will be gathered considering different generation times across taxa.

I will focus on community stability and will build a Bayesian model incorporating climatic factors (e.g., variability, skewness, range of maximum and minimum of temperature-distribution over the years etc.). While scientists studied thermophilization in the context of warming-related turnover in communities, no predictive model for community stability has been developed, to date, assessing the effect of extreme climatic events across taxa using a global database. This study will inform the current status of communities across multiple taxa facing climatic extremes and help prioritize conservation efforts (see Work Package 2).

I will gather annual climate data (mean, minimum, maximum for temperature, rainfall) and compute the variability, and the skewness of their distribution for the study period over which the community dynamics was studied. I will compute the richness (number of total species and dominant species that were present minimum 70% of the total years sampled), variance ratio, community level total tail association from pairwise synchrony as drivers. These drivers appeared as significant for explaining variation in community stability from my recent study (manuscript in preparation). I will compute the response variable community stability as the inverse of community-variability over the study period. Then, I will build a Bayesian model to see the effect of climate parameters, on the stability-driver relationships for different taxa.

2 Data

2.1 Data structure

Total 1948 community timeseries we have collected for the timespan 1979-2019. 4 taxa are considered - birds, fish, freshwater invertebrates, terrestrial invertebrates. Below is the summary of the datatable. Description of each column is given in README.txt

## 'data.frame':    1925 obs. of  47 variables:
##  $ source          : chr  "BBS" "BBS" "BBS" "BBS" ...
##  $ STUDY_ID        : chr  "Northern Pacific Rainforests" "Central Rockies" "Fraser Plateau" "Fraser Plateau" ...
##  $ newsite         : chr  "124_11_126" "124_11_208" "124_11_222" "124_11_244" ...
##  $ REALM           : chr  "Terrestrial" "Terrestrial" "Terrestrial" "Terrestrial" ...
##  $ TAXA            : chr  "birds" "birds" "birds" "birds" ...
##  $ ORGANISMS       : chr  "Birds" "Birds" "Birds" "Birds" ...
##  $ initR           : int  88 119 120 116 110 105 83 91 109 125 ...
##  $ nsp             : int  33 65 36 52 49 50 32 41 42 61 ...
##  $ nyr_used        : int  22 23 22 23 23 21 22 20 22 20 ...
##  $ startyr         : int  1997 1997 1997 1997 1997 1997 1997 1998 1997 1997 ...
##  $ endyr           : int  2019 2019 2018 2019 2019 2019 2019 2019 2019 2017 ...
##  $ nint            : int  528 2080 630 1326 1176 1225 496 820 861 1830 ...
##  $ nind            : int  435 1837 564 1165 944 1027 410 658 728 1612 ...
##  $ npos            : int  56 143 50 100 137 152 71 89 93 131 ...
##  $ nL              : int  27 62 24 44 50 107 33 36 40 59 ...
##  $ nU              : int  29 81 26 56 87 45 38 53 53 72 ...
##  $ nneg            : int  37 100 16 61 95 46 14 73 40 87 ...
##  $ L               : num  2.75 7.2 2.1 4.75 4 ...
##  $ U               : num  -2.79 -8.87 -2.7 -7.05 -11.35 ...
##  $ f_nind          : num  0.824 0.883 0.895 0.879 0.803 ...
##  $ f_nL            : num  0.0511 0.0298 0.0381 0.0332 0.0425 ...
##  $ f_nU            : num  0.0549 0.0389 0.0413 0.0422 0.074 ...
##  $ f_nneg          : num  0.0701 0.0481 0.0254 0.046 0.0808 ...
##  $ cvsq_real       : num  0.0201 0.0106 0.0382 0.0193 0.048 ...
##  $ cvsq_indep      : num  0.00804 0.00553 0.01337 0.00829 0.01569 ...
##  $ phi             : num  2.5 1.92 2.86 2.33 3.06 ...
##  $ phi_LdM         : num  0.1033 0.0459 0.1349 0.0727 0.1406 ...
##  $ skw_real        : num  0.361 -0.262 0.684 0.651 0.194 ...
##  $ skw_indep       : num  0.18 0.187 0.352 0.555 0.32 ...
##  $ phi_skw         : num  2.004 -1.405 1.94 1.174 0.606 ...
##  $ iCV             : num  7.05 9.71 5.12 7.2 4.56 ...
##  $ iCValt          : num  5.42 8.57 3.32 7.16 2.53 ...
##  $ LONGITUDE       : num  -125 -120 -122 -121 -123 ...
##  $ LATITUDE        : num  50 49.6 50.9 52.5 53.9 ...
##  $ t_med           : num  2837 2825 2806 2790 2787 ...
##  $ tmax_med        : num  2876 2869 2861 2840 2838 ...
##  $ tmin_med        : num  2802 2774 2749 2745 2740 ...
##  $ t_skw           : num  0.615 0.929 0.961 0.749 0.141 ...
##  $ tmax_skw        : num  -0.0659 0.5457 0.1801 0.2232 -0.1224 ...
##  $ tmin_skw        : num  0.583 0.858 0.874 0.747 0.272 ...
##  $ t_var           : num  375 361 284 366 279 ...
##  $ trend_t_tau     : num  -0.026 -0.026 -0.026 -0.026 -0.026 ...
##  $ trend_t_tau_sig : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ t.lm.slope      : num  0.3553 0.6243 0.6433 0.0785 -0.1765 ...
##  $ t.lm.slope.sig  : int  0 1 1 0 0 1 0 0 1 1 ...
##  $ t.sens.slope    : num  0.3889 0.5476 0.5931 0.0389 -0.2722 ...
##  $ t.sens.slope.sig: int  0 1 1 0 0 1 0 0 0 0 ...

But see the below table which shows the sample size for each taxa and the datasource, we have very few sample size for terrestrial invertebrates. I feel it’s better to write a paper about north american birds vs european fish (atleast we have >500 datapoints for birds and fish). But I am open to other ideas. I don’t know which kind of data requirement we need for response diversity, but if we can have the body size or biomass (as trait) data then I can test the H0: whether response diversity increases the stability or influenced by temperature?

## # A tibble: 12 × 3
##    TAXA                      source              n
##    <chr>                     <chr>           <int>
##  1 birds                     BBS              1227
##  2 birds                     BioTIME             8
##  3 fish                      BioTIME             3
##  4 fish                      BioTIMEx           25
##  5 fish                      RivFishTIME       544
##  6 freshwater invertebrates  BioTIME            11
##  7 freshwater invertebrates  BioTIMEx            2
##  8 freshwater invertebrates  InsectRoel         79
##  9 freshwater invertebrates  SwissLakeZoo        5
## 10 freshwater invertebrates  Zooplankton2014     7
## 11 terrestrial invertebrates BioTIME            11
## 12 terrestrial invertebrates BioTIMEx            3

2.2 Sitemap for each taxa

3 Methods

I want to see how community stability-drivers relationship would affect by the changing environmental variable (annual temperature distribution). Temperature could vary in many ways (see 3.1). I am considering three aspects of environmental (temperature) timeseries here: median of annual temperatures (\(t_{med}\)) during the study periods, trend (\(t_{trend}\)) and skewness (\(t_{skw}\)) of annual temperature timeseries for a given community. My intuition is:

• community stability would be affected by any of these temperature component either directly or indirectly via the drivers.
• As \(t_{med}\), \(t_{trend}\) changes, diversity-stability relationship should be affected, so stability would change via portfolio effect. e.g. terrestrial plants, beetles, and vertebrates show declining richness with incresing temperature in the past studies.
• Similarly, changing \(t_{med}\), \(t_{trend}\) should relate how species interactions get modified in a changing environment. For example, as temperature increases (or decreases) \(t_{med}\), community might loose some species, and might be dominated by fewer species which may or may not be synchronous, depending on the species-traits at that particular environment. But if \(t_{trend}\) increases, the community is exposing to warmer environment with years, then maybe warm adapted species will become dominant and species with similar traits can have higher synchrony. I am not sure, what will happen, but we can see how community-level response (avg of all species’response to warming in that community) changes with temperature?
• Changing \(t_{trend}\), \(t_{skw}\), means frequent extreme events (like heatwaves, or cold winter), and it should be related to tail-dependent synchrony, where pairwise synchrony between species gets stronger beyond a certain threshold.

Figure 3.1: Temperature timeseries figure

Figure 3.2: Temperature timeseries figure with real data

3.1 Variables estimated and modelled

(Perhaps make this into a table.)

Let \(N_{i,t,s}\) be the abundance (sometimes it was biomass data only if abundance data were not available) of species \(i\) at time \(t\) at site \(s\). Total abundance at time \(t\) at site \(s\) is \(N_{t,s} = \sum_{i=1}^{s} N_{t,s,i}\).

Community stability at site \(s\) was estimated as the inverse of the coefficient of temporal variation in total community biomass ?or? abundance: \(TempStab_s = 1 / CV(N_{t,s}) = median(N_{t,s}) / IQR(N_{t,s})\)

Species richness at site \(s\) was estimated as the number of total species and dominant species that were present minimum 70% of the total years sampled.

Comunity variance ratio: a measure of synchrony, scaled between 0 to 1 (Loreau & Mazancourt).

Community level total tail association from pairwise synchrony: see BioDyn project, Figure 1.

Temperature median: Median of CHELSA-extracted annual temperature timeseries for the study years included in the analysis for each community.

Temperature trend: Monotonic trend of annual temperature timeseries (computed by non-parametric Sen’s method or parametric linear fit slope).

Temperature variability: Temperature variability for the community during the study period = median(annual temperature)/IQR(annual temperature distribution for the study period).

Temperature skew: Skewness of CHELSA-extracted annual temperature timeseries for the study years included in the analysis for each community.

4 Results

4.1 Community stability exploration

Figure 4.1: Stability-diversity relationship for birds and fish.

4.1.1 Birds

Figure 4.2: Stability-diversity relationship for birds at different temperature levels

Figure 4.3: Stability-temperature relationship for bird communities at different richness levels

Figure 4.4: Stability-synchrony relationship for birds at different temperature levels

Figure 4.5: Synchrony-temperature relationship (scatterplot)

Figure 4.6: Synchrony-temperature relationship (boxplot)

Figure 4.7: Synchrony richness relationship.

Figure 4.8: Synchrony temperature relationship.

Figure 4.9: Stability - temperature skew relationship.

4.1.1.1 Basic statistics for birds

Model of bird stability:

term	estimate	std.error	statistic	p.value
(Intercept)	27.1928	9.0357	3.0095	0.0027
log2(nsp)	-4.2670	1.7386	-2.4543	0.0143
t_med	-0.0097	0.0032	-3.0436	0.0024
log2(nsp):t_med	0.0017	0.0006	2.7109	0.0068

Model of bird synchrony:

term	estimate	std.error	statistic	p.value
(Intercept)	-13.0349	10.4663	-1.2454	0.2132
log2(nsp)	1.7048	2.0139	0.8465	0.3974
t_med	0.0047	0.0037	1.2647	0.2062
log2(nsp):t_med	-0.0008	0.0007	-1.1208	0.2626

4.1.1.2 Bird conclusions

Bird communities display a positive richness stability relationship. This relationship is stronger at higher temperatures. Equally, high richness bird communities are more stable at higher temperatures, while low richness bird communities are less stable at higher temperatures.

There is some suggestion that this may be explained by synchrony, but the statistics show no strong associations of synchrony with \(t_med\) or synchrony.

4.1.2 Fish

Figure 4.10: Stability-diversity relationship at different temperature levels

Figure 4.11: Stability-temperature relationship at different richness levels

Figure 4.12: Stability-synchrony relationship at different temperature levels

Figure 4.13: Synchrony-temperature relationship (scatterplot)

Figure 4.14: Synchrony-temperature relationship (boxplot)

Figure 4.15: Synchrony richness relationship.

Figure 4.16: Synchrony temperature relationship.

Figure 4.17: Stability - temperature skew relationship.

4.1.2.1 Fish basic statistics

Model of fish stability:

term	estimate	std.error	statistic	p.value
(Intercept)	-20.4100	5.1952	-3.9286	0.0001
log2(nsp)	7.9863	2.4723	3.2303	0.0013
t_med	0.0073	0.0018	3.9649	0.0001
log2(nsp):t_med	-0.0028	0.0009	-3.2467	0.0012

Model of fish synchrony:

term	estimate	std.error	statistic	p.value
(Intercept)	7.6481	4.1111	1.8603	0.0634
log2(nsp)	-2.2569	1.9564	-1.1536	0.2492
t_med	-0.0029	0.0015	-1.9623	0.0502
log2(nsp):t_med	0.0007	0.0007	1.0253	0.3057

4.1.2.2 Fish conclusions

Fish communities display a positive richness stability relationship at low temperature, and a negative one at higher temperatures. This is the opposite of the interaction pattern for birds, where the relationship became more positive when temperature was higher. Equally, high richness fish communities are slightly less stable at higher temperatures, while low richness fish communities are more stable at higher temperatures (again the opposite to the bird patterns).

Not sure, at present, how much can be explained by synchrony, but the statistics show no strong associations of synchrony with t_med or richness.

Which pattern / finding are we trying to explain with the following two graphs?

Figure 4.18: Distribution of temperature skewness, birds and fish together.

Figure 4.19: Distribution of temperature skewness, birds and fish separate. Fish communities generally experience more negatively skewed temperature fluctuations. In the fish SEM we see that t_skw directly affects stability, with more positive skew being associated with less stability. No evidence of association of t_skw and stability in birds.

Figure 4.20: Distribution of temperature trend estimated by non-parametric Sen’s slope, and parametric linear fit slope. Colored points are significant Sen’s slope (green: birds, blue: fish) .

## 
##  Freshwater Terrestrial 
##   0.3391608   0.2493927

Figure 4.21: Histogram plot for trends, both taxa.

Figure 4.22: Histogram plot for significant trends, both taxa.

4.2 Explanations

So, from the exploratory plots we can see: at higher temperature positive stability-diversity relationship becomes stronger for birds but for fish it becomes weaker. Also fish becomes more asynchronous with increasing temperature. So, why does that happen? to find this we could explore how much the bird species and fish species are consistent to temperature change across all communities.

The cue is: if fish species are not much consistent in their response to warming and vary across sites, that means you cannot make a conclusion that they would become similar with changing temperature. On another note, bird species should be more consistent towards warming if their is no change in their synchrony level across communities. Another possibility could be with changing temperature you might loose some species (its not just number of individuals, it will selectively prefer few species with better fitness), and then the communities will be dominated by few species with similar traits (so increasing synchrony). we will test this below.

From the above plots, we can see birds are showing consistent response-distribution across all temperature change, i.e., in either end of temperature spectrum (low or high end). That’s why the synchrony level remains similar for birds. But for fish, warming increases the richness (addition of new species), and as fish species now become more variable in response to temperature sensitivity (trait-variation), they show more asynchrony compared to low temperature scenario where only few species exists (see smaller circle size on the map for lowT,<50%CI) and show similar traits (so more synchrony). Note: when I show this to Frank, he commented on how much robust is the pattern for fish at low T as there are only few species existed across 145 sites - so it also depends on how we considered the lowT-highT communities. I set beyond 50% CI of temperature range as low/high. Even if I decrease that to 30% CI, still very few species found in low T sites (15 sp across 203 sites: 80% >0, 20% <0 line).

To further explore this idea: we collected traits data for birds and fish species used in the analysis. For fish-traits, I will use body length measurements, for bird-traits I will use HWI (Hand-wing index). From below figures: at high T, birds have slightly less dispersal ability (lower HWI), but richness is more or less uniformly spread at either temperature range. For fish, at lowT, few large species exists with similar traits (remember the previous histogram plot 90-10) showing higher synchrony, as temperature increases addition of new small fishes in the community (maybe better environment for them to exist in that temperature rather than too cold water) makes them asynchronous with more trait variation (histogram plot 66-34).

When I showed this to Blake, he was not convinced by the idea to split the data into two: low/high based on t_med (to him this temperature difference is more on latitudinal differences as shown in the map), and same species can exist in both communities - so why changing t_med should change the synchrony level for fish? and getting different bodysize fish from low/high t_med (fewer big fish in lowT and many smaller fish in highT) is not explaining why big fish should be more synchronous - is it because of fewer species (richness) or because bigger fish abundance change needs more time - not on annual scale?

So, I thought to make a plot of how community-level average response traits (average of standardised correlation between species abundance with t_med timeseries across sites) changes with increasing temperature (t_med)? For fish, it should decrease with increasing t_med, whereas for birds it should be a flat relationship.

Possible explanation:

Figure 4.23: Response variation with temperature

Now, we will do a path analysis for a simplistic mixed effect model to see the environmental effects on community stability for both taxa.

So, from the path analysis, what do we see for birds -

• for birds: increasing temperature \(t_{med}\) decreases community stability, though it has no significant direct effect on the drivers (like richness, synchrony).
• increasing temperature trend also has no significant effect on birds.
• increasing extreme heatwaves decreases tail dep synchrony. Here direct effect of t_skw is not significant on stability, as all bird data have equal proportion of +ve and -ve skewness (see above plot). But still tail dependent synchrony is important mechanism for stability, especially for terrestrial taxa (we found this from BioDyn project), and driven by the skewness of temperature time series (extreme events).
• positive diversity-stability relationship and negative synchrony-stability relationship are observed as expected.

and for fish -

• overall synchrony (variance ratio) is the important determinant for stability (this we knew from BioDyn project findings), as it connects the environmental effects to stability.
• increasing \(t_{med}\) increases richness, and more asynchrony (-ve effect on VR), which is also consistent with more variable traits for the fish species.
• for fish, extremes has direct negative effect on stability, not indirect effect through tail-dep synchrony as it is not important driver for freshwater as we found from BioDyn.

Why I did not choose t_var (variability in temperature timeseries) in the path model? As I already have added the t_med as one of the variable in the path model, including again it as t_var would increase the multi-collinearity (as increasing VIF). Also we added the t_skw, so together with t_med, it should give you an estimation of whole temperature timeseries distribution - and would be better as directional metric (positive or negative skewness) than just the variability (non-directional).

[I separately ran models replacing t_med with t_var (see graphs below): for birds no environmental effects, for fish I found increasing variability decreases richness.]

5 Discussion